Monte-Carlo Computer Algorithm for the Efficient Simulation of Nanoscale Thermal and Dynamic Properties of Complex Materials

Ralph Chamberlin (Inventor)

Research output: Patent

Abstract

In the past 50 years, computer simulations have emerged as a powerful technique for investigating the physical properties of complex systems. There are two principal types of simulations, molecular dynamics (MD) and Monte Carlo (MC). MD simulations are usually based on fundamental physical principles, such as conservation of energy and/or conservation of momentume, wheas MC is usually optimized for computational efficiency. Althought some MC simulations have been developed that inclused conservation of momentum, most still utilize the canonical ensemble where energy is not conserved. A key prior art is Creutz MC simulation of the ising model in the microcanonical ensemble, but this model does not address momentum considerations. Here a novel family of Ising-like MC algorithms that incorporate both conservation of energy and conservation of momentum.The Ising model is the simplest model for the thermal behavior of interacting particles. The simplicity comes from assuming that the particles are fixed to a lattice, and that they have only two allowed states. Originally the model was applied to magnetic spins that may be either up or down; but the model may also apply to other binary degress of freedom such as bits that are 1 or 0, lattice sites that are occupied or empty, or molecular desplacements that are left or right. Despite its simplicity, the standard Ising model exhibits several features that are similar to more realistic models, especially near a transition where fluctuations are averages over long length scales. Another novel feature of the MC algorithms described here is that a broad range of realistic behavior is obtained by averaging fluctuations over long time scales. Furthermore, the ("nanothermodynamics"), thus providing a new paradigm for simulating the thermal and dynamic properties of complex systems on the scale of nanometers.The most important concept from nanotherodynamics for computer simulations is the careful considerations of the various thermal ensembles and their fluctuations. In the usual therodynamics limit of infinitely many particles, fluctuations that scale as 1//N are negligible, and all ensembles yeidl similar results. However when N
Original languageEnglish (US)
StatePublished - Jun 3 2004

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dynamic characteristics
conservation
thermodynamic properties
Ising model
complex systems
momentum
simulation
computerized simulation
molecular dynamics
arts
energy
physical properties

Cite this

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abstract = "In the past 50 years, computer simulations have emerged as a powerful technique for investigating the physical properties of complex systems. There are two principal types of simulations, molecular dynamics (MD) and Monte Carlo (MC). MD simulations are usually based on fundamental physical principles, such as conservation of energy and/or conservation of momentume, wheas MC is usually optimized for computational efficiency. Althought some MC simulations have been developed that inclused conservation of momentum, most still utilize the canonical ensemble where energy is not conserved. A key prior art is Creutz MC simulation of the ising model in the microcanonical ensemble, but this model does not address momentum considerations. Here a novel family of Ising-like MC algorithms that incorporate both conservation of energy and conservation of momentum.The Ising model is the simplest model for the thermal behavior of interacting particles. The simplicity comes from assuming that the particles are fixed to a lattice, and that they have only two allowed states. Originally the model was applied to magnetic spins that may be either up or down; but the model may also apply to other binary degress of freedom such as bits that are 1 or 0, lattice sites that are occupied or empty, or molecular desplacements that are left or right. Despite its simplicity, the standard Ising model exhibits several features that are similar to more realistic models, especially near a transition where fluctuations are averages over long length scales. Another novel feature of the MC algorithms described here is that a broad range of realistic behavior is obtained by averaging fluctuations over long time scales. Furthermore, the ({"}nanothermodynamics{"}), thus providing a new paradigm for simulating the thermal and dynamic properties of complex systems on the scale of nanometers.The most important concept from nanotherodynamics for computer simulations is the careful considerations of the various thermal ensembles and their fluctuations. In the usual therodynamics limit of infinitely many particles, fluctuations that scale as 1//N are negligible, and all ensembles yeidl similar results. However when N",
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AB - In the past 50 years, computer simulations have emerged as a powerful technique for investigating the physical properties of complex systems. There are two principal types of simulations, molecular dynamics (MD) and Monte Carlo (MC). MD simulations are usually based on fundamental physical principles, such as conservation of energy and/or conservation of momentume, wheas MC is usually optimized for computational efficiency. Althought some MC simulations have been developed that inclused conservation of momentum, most still utilize the canonical ensemble where energy is not conserved. A key prior art is Creutz MC simulation of the ising model in the microcanonical ensemble, but this model does not address momentum considerations. Here a novel family of Ising-like MC algorithms that incorporate both conservation of energy and conservation of momentum.The Ising model is the simplest model for the thermal behavior of interacting particles. The simplicity comes from assuming that the particles are fixed to a lattice, and that they have only two allowed states. Originally the model was applied to magnetic spins that may be either up or down; but the model may also apply to other binary degress of freedom such as bits that are 1 or 0, lattice sites that are occupied or empty, or molecular desplacements that are left or right. Despite its simplicity, the standard Ising model exhibits several features that are similar to more realistic models, especially near a transition where fluctuations are averages over long length scales. Another novel feature of the MC algorithms described here is that a broad range of realistic behavior is obtained by averaging fluctuations over long time scales. Furthermore, the ("nanothermodynamics"), thus providing a new paradigm for simulating the thermal and dynamic properties of complex systems on the scale of nanometers.The most important concept from nanotherodynamics for computer simulations is the careful considerations of the various thermal ensembles and their fluctuations. In the usual therodynamics limit of infinitely many particles, fluctuations that scale as 1//N are negligible, and all ensembles yeidl similar results. However when N

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